Short Circuit Stress Calculation in Power Transformer Using Finite ...

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)

Short Circuit Stress Calculation in Power Transformer Using Finite Element Method on High Voltage Winding Displaced Vertically Ashfaq Ahmad1, Iqra Javed2, Waseem Nazar3 1,3

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The University of Lahore Department of Electronics University of Management and Technology Department of Informatics and Systems Data collected from the High Voltage testing laboratory shows that one fifth of the transformers under test are failed due to weak insulation which ultimately bear short-circuit current. It is important to mention that the transformers which have to undergo this test, are manufactured with almost and special care in the manufacturer‘s premises [9, 10]. Lack of insulation strength of transformers imposed by manufacturers can cause severe damages to the transformer as well as the system. System disruption include following effects;

Abstract— The objective of this research is to compute the mechanical stresses in power transformer resulting from the currents more than rated value during its operation. Due to this high fault current, mechanical stresses are produced indifferent directions which may cause the damage of winding insulation. Various techniques have been adopted to analyze the stresses on transformer windings. For the accomplishment of research, FEM (Finite Element Method) is utilized for the calculation of short circuit forces. All mechanical generated in transformers are calculated mathematically and verified through software. For the verification of results, real time measurements on 20MVA 132 /11.5KV power transformer are made. Various failure mechanisms due to these forces have been discussed. Moreover, design parameters which determine the maximum stresses in different parts of the transformer are also the part of research. Effects of asymmetrical current and forces in various parts of transformer have also been narrated. Moreover, Different properties of materials have been studied and the usage of proper material for withstanding the dynamic effects of short circuits is discussed. Workmanship errors on short circuit withstand capability have also been elucidated. Finally, a complete model for the study of dynamic effects of short-circuits in a power transformer and comparison with forces calculated with FEMM soft ware [13].

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Deformation of LV and HV windings Broken pressure plates on windings Bending of clamping structure Bulging of tank body Collapse of bushings Short-Circuited tapping leads

Rest of the paper organized as follows; Section-II discusses types of short circuits in power system, section –III narrates the forces which are produced due to short circuit current while remaining sections include axial and radial forces acting on windings, and last section describes the fem calculations results of forces acting on transformer windings [5].

Keywords— Finite element method; Power transformer; Short circuit stress; Mechanical Stresses; Axial and Radial Stresses.

II. SHORT CIRCUIT CURRENTS Almost all types of faults cause the sudden rise of current in power system which results in malfunction and inconsistent operation of installed equipment along with severe effect on transformer insulation. Usually, the three-phase faults are the most severe of all; hence the transformer should be designed to withstand the effects of symmetrical three phase faults. It must be mentioned here that in some cases (Where a tertiary connected winding is present), the single-phase to line fault short-circuit current can be higher than the three-phase fault on those windings, since it is related to very special cases, emphasis is made on symmetrical three-phase faults only.

I. INTRODUCTION Due to continuous growth in demand of electricity, Government and utility companies have started expansion of generation stations which include interconnections of national grids. Due to these additions, the short circuit current of the system has increased where many sources of power are available to feed faulty location on the occurrence of event. All the components in the system are affected by this change including transformers which have to bear heavy currents. A large number of transformers in power system have been reported to fail due to prolonged heavy current. 301

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013) A. Value of symmetrical short-circuit current For three-phase transformers with two separate windings, the r.m.s value of the symmetrical short-circuits current ―I‖ shall be calculated as in equation (i) [1]. (i) Where:

Fig.2 A Sinusoidal voltage source switched on to an RL network

The mechanical strength of the transformer windings should be such that it shall withstand the highest shortcircuit forces generated which correspond to the first current peak in the figure above, since this current peak has the highest magnitude due to presence of DC component in the current pattern.

U: is the rated voltage of the winding under consideration, in Kilovolts Zt: is the short-circuit impedance of the transformer referred to the winding under consideration, in ohms per phases Zs: is the short-circuit impedance of the system, in ohms per phase As mentioned above, due to addition of more and more generating stations within an interconnected system, the source impedance Zs is very small and generally neglected for calculations purpose.

C. Thermal withstand during short-circuit During short-circuit, a very high current flows within the windings of the transformer. However, the duration of short-circuit is very small, the temperature of the windings generally do not rise high enough to damageable values. Hence, this effect can generally be neglected. IEC 60076-5 however, gives a formula for the calculation of temperature rise during short-circuits. This formula assumes that all the heat produced by the winding during short-circuits stays in it and none is dissipated. This is a poor assumption, but since the limit of allowable temperature rise is high (250oC), almost all the transformers qualify this requirement during short-circuit testing. According to IEC 60076-5, the average temperature Ө1attained by the winding after short circuit is calculated by the equation (ii) [2].

B. Nature of short-circuit current Consider the circuit given alternate voltage source. Assuming that the below with an switch is closed at t=0 instant, which simulates the short-circuit, the expression for the current i(t) can be written as follows:

Fig 1A Sinusoidal voltage source switched on to an RL network

(ii)

i(t) = Imax[sin(ώt-Ө)] Where: Imax: Maximum value of the current i t: Time, in seconds Ө: Phase angle of the circuit impedance [tan-1(ⱷL/R)] Ʈ: Time constant [L/R] The plot of this current expression with respect to time is as under:

Where Өo: is the initial winding temperature, in degrees Celsius J: is the short-circuit current density, t: is the duration, in seconds (s)

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)  Position of tank causes the leakage flux pattern to change which is again ignored in the analytical formula of short-circuit forces calculations.  Portion of windings under the yoke have a different leakage field pattern compared to portion outside the window. Again this phenomenon is ignored in the analytical formula.  Effect and presence of mechanical bracings of the windows is ignored in the analytical formula.  Combined (axial and radial) forces at the winding ends which are the major cause of tilting of the conductors are neglected in analytical formula.  Axial imbalance of windings during manufacturing is neglected in the analytical method of forces calculation. This imbalance usually occurs during shifting over of windings over the core where the centerline of windings is not exactly the same.  Axial imbalance within the winding (which is normally due to presence of radial spacers in the windings) is ignored. During manufacturing of winding on the winding machines, height of windings has to be maintained by placement of radial spacers within it. The position of placement of these stabilization spacers can shift the centerline of the winding which cannot be ignored.

III. SHORT-CIRCUIT FORCES When a current carrying conductor lies in a magnetic field, a force is produced upon that current carrying conductor, whose magnitude is given by equation (iii).

F=B.I.L sinα

(iii)

Where: B: I: L: α:

flux density, in Tesla Current in the conductor, in Amps length of current carrying element, in meters angle between flux density vector and current vector

This force is called the ―electromagnetic‖ force because it is produced both by combined effect or electric current and magnetic flux. [12] The direction of this force can be easily computed using the well-Known ―Left-hand rule‖. A. Electromagnetic Forces In transformers, electromagnetic forces may have three components if we model it in 3D cylindrical coordinates.  r-component  z-component  ᶲ-component The r-component of the electromagnetic forces results in the radial forces that act on the windings [8]. The zcomponent is the originator of the axial forces that act on the windings. Finally, the ᶲ-component can cause twisting motion of the windings, but it is never present because the center axis of the windings is always coinciding with each other. The conventional way to calculate the short-circuit forces is by solving equation (iii), using data of the transformer from the design calculation sheets. This calculation, however, assumes a lot of data which can sometimes result in a very safe calculation and, else wise, could result in unsafe margins during calculations.

IV. FINITE ELEMENT MODELING A. Introduction to finite element method Finite element method (FEM) is a numerical method mainly used for solving Differential and Integral Equations. Essence of this method is to divide the application domain in very small sub domain elements called as finite elements. Problem is subdivided into Finite size sub problems and is independently dealt to find complete problem solution. There are many software commercially available incorporating the Finite Element Method Solution. In this thesis, a software tool titled meshing and finite element solver has been used [3]. The model has been drawn using MATLAB with complete computation of leakage flux and therefore short-circuit forces.

B. Approximations in analytical formula The analytical method of calculating the short-circuit forces assumes certain data, most prominent of which are:  Conductors are tightly wound radially on top of each other and thus the radial short-circuit forces act over the average circumference of the windings.  Presence of axial cooling ducts can result in appreciable error in the short-circuit forces calculations which is ignored in the analytical formula [8].

B. Finite element method in transformer In transformers, finite element method can be used to calculate the following quantities:  Eddy currents and winding stray losses  Electric field analysis

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)  Temperature gradient calculations  Short-circuit stresses  Stress-strain analysis of the clamping structure C. Steps of finite element modeling. Finite Element modeling is a highly accurate method of calculating the transformer parameters. The FEM formation makes use of the fact that poison‘s partial-differential equation is satisfied when total magnetic energy function is a minimum [4]. 1- The geometry to solve (which is basically the core and set of transformer winding represented simple as rectangular blocks) can be drawn using most CAD programs. In this work, Auto Cad 2010 is used to drawn the geometry in .dxf format. 2Fig. 4 Meshing of the transformer geometry

4- The properties of each of the blocks drawn, is then assigned along with the boundary conditions. Since core has a very high relative permeability value, it will not store any appreciable energy. Hence, it doesn‘t matter whether core is given a relative permeability of 10,000 or 100,000. When assigning the properties to the windings, it must be made sure that the ampere-turns of all the winding regimes must be equal and opposite, so that no mutual component of flux in the core should exist. 5- The space filled with oil is assigned a relative permeability of 1, including the windings. 6- The geometry is solved in the FEM solver and the flux leakage plot obtained:

Fig. 3 Geometry of the transformer

3- Once the geometry is ready, it is then divided in to finite elements i.e. small elements. The smaller the size of each mesh or element, the higher will be the accuracy of the results can be obtained if problem is divided into number small problems. Different models and geometries of transformer for the application and calculations are given in fig 4, 5, 6 and 7. while fig. 8 and 9 gives flux plots of transformer which are important to obtain while calculating short circuit effect on power transformer windings.

Fig. 5 Flux pattern of a transformer

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013) V. ANALYSIS ON STRESSES BASED ON VERTICAL MOVEMENT

The geometries are solved in the FEM solver software and the flux leakage plots obtained as in fig.8.

Analysis of HV winding in vertical of power transformer performed. The winding rotation steps were chosen arbitrary as per design approach. The movement step is 0-mm, 2-mm, 5mm, 10-mm, 15-mm is chosen for vertical respectively. The results and geometry model for these movements are given as below in fig.6.

Fig. 8 Flux plot

Following is the comprehensive simulation results of fluxes obtained from FEM measured forces obtained from FEMM by setting properties of core, oil, LV, HV windings etc. It also includes comparison plots of forces obtained by mat lab. There are number of findings from the simulation results of FEMM.

Fig. 6 Geometrical model

Fig.7 Gives mesh model in these cases would be displaced in vertically as shown below

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The direction of short-circuit flux (arrows in the fig.) Total effect of the forces appears to cancel out. Forces at the winding centre are purely radial. Inner winding is subject to buckling effect. Outer winding tends to stretch out. Forces at the winding ends have both axial and radial direction [7, 11]. The flux simulation results at vertical movement are given below which are extracted from [6,7].The minimum flux density is shown with light color while maximum flux density is present at top middle and bottom turns of winding. Different colors show the level of flux produce in windings followed by measurement of H.V and L.V forces at bottom and in different positions in windings with the help of FEM. Results are concluded by comparing the results of FEMM and measurements made mathematically. In given below flux density plots as in fig. 9, various levels of flux densities are presented by different colors.

Fig. 7 Mesh model

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013)

Fig. 11 Comparison of HV forces in windings

From above plot it is clear that in early turns the negative forces are dominant and in middle of the turns the forces approach to zero because of cancelation of effect of the negative and positive forces. This force applied on winding pattern is same for the displacements of 0-mm, 2mm and 15-mm. The only difference is the windings having less displacement has tendency of negative forces to approach from negative to zero more quickly and forces approach from zero to positive more slowly and vice versa. The left side of the above plot of fig.11 is the forces plot when high voltage winding displaced at 5-mm and 10-mm, it is clear that in early turns the negative forces are dominant and the middle turn positive forces are dominant, in the last turns forces are approach positive to negative and saturated. The Fig.10 and Fig.11 shows the complete comparison plots of LV and HV forces in windings at different displacement. The Fig.12 and Fig.13 shows the individual plots of forces in winding at different displacements 0-mm, 2-mm, 5-mm, 10-mm and 15-mm respectively.

Fig. 9 Flux density plot

VI. VERTICAL WINDING FORCES The comparison plot of LV forces in windings at different displacement is given below in fig. 10.

Fig. 10 Comparison of LV forces in winding

From the above plot in fig. 10, it is clear that in early turns the negative forces are dominant and in middle of the turns the forces approach to zero because of cancelation of effect of the negative and positive forces. This force applied on winding pattern is same for the displacements of 0-mm, 2-mm and 15-mm. The only difference is the windings having less displacement has tendency of negative forces to approach from negative to zero more quickly and forces approach from zero to positive more slowly and vice versa. The left side of the above plot of fig.10 is the forces plot when high voltage winding displaced at 5-mm and 10-mm, it is clear that in early turns the negative forces are dominant and the middle turn forces approach negative to positive, in the last turns again negative forces are dominant. The comparison plot of HV forces in windings at different displacement is given below in fig. 11.

Fig.12 Individual LV forces in winding at different displacement

Fig.13 Individual HV forces in winding at different displacement

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 11, November 2013) A. x-axis forces at winding The comparison plot of LV forces at bottom of windings at different displacement is given below in fig. 14.

The accumulated force increases from zero to a constant maximum value earlier at winding having less displacement and decreases from maximum value to zero late in bottom turns and vice versa for windings with more displacement. This force applied on winding pattern is same for the displacements of 0-mm, 2-mm and 15-mm. The forces plot when high voltage winding displaced at 5-mm and 10-mm, it is clear that in early turns the positive forces are dominant and the middle turn negative forces are dominant, and in the last turns forces are approaches to zero. The Fig.16 and Fig.17 shows the individual plots of forces at winding on different displacements 0-mm, 2-mm, 5-mm, 10-mm and 15-mm.

Fig. 14 Comparison of LV forces At windings

From the above plot it is clear that accumulated forces are minimal in upper and bottom turns. Whereas accumulated force is maximum at middle turns of windings. The accumulated force increases from zero to a constant maximum value earlier at winding having less displacement and decreases from maximum value to zero late in bottom turns and vice versa for windings with more displacement. This force applied on winding pattern is same for the displacements of 0-mm, 2-mm and 15-mm. The forces plot when high voltage winding displaced at 5mm and 10-mm, it is clear that in early turns the positive forces are dominant and the middle turn negative forces are dominant, and in the last turns forces are approaches to zero and saturated The comparison plot of HV forces at bottom of windings at different displacement is given below in fig.15.

Fig.16 Individual LV forces in winding at different displacement

Fig.17 Individual HV forces in winding at different displacement

VII. CONCLUSIONS The results of mechanical forces generated due to prolonged high currents in power transformer windings have been evaluated. High temperatures generated inside transformer may puncture its insulation which causes breakdown. As Power transformer is very expensive power system apparatus which is needed to be protected with first priority. That is why its failure avoided and comprehensive analysis is done to cater all drastic situations which may cause its complete failure. This research will enable the transformer manufacturers for careful design of transformer and the power utility authorities to ensure its safe operation in power system.

Fig. 15Comparison of HV forces at windings

From the above plot it is clear that accumulated forces are minimal in upper and bottom turns. Whereas accumulated force is maximum at middle turns of windings.

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